Of course, since the goal is to predict \(Y_{n+1}\) , its value is not observed, so the above calculations cannot exactly be carried out. However, the exchangeability-preserving properties of the transformations described above provide a procedure to suitably rank candidate values \(\tilde{y}\)  of \(Y_{n+1}\)  based on the observed \(Y^n=y^n\) ; see Algorithm REF . The output of this algorithm is a data-dependent function \(\tilde{y} \mapsto \pi (\tilde{y}; y^n)\)  whose interpretation is as a measure of how plausible is the claim “\(Y_{n+1}=\tilde{y}\) ” based on data \(y^n\) . In [1]}, this function is referred to as a “p-value” (p. 25) or as a “conformal transducer” (p. 44), but we prefer the name plausibility contour for various reasons, one being that its interpretation is clear. One important role the plausibility contour plays is in the construction of conformal prediction regions. Indeed, the family of sets defined by
\({P}_\alpha (y^n) = \lbrace y_{n+1} \in \mathbb {Y}: \pi (y_{n+1}; y^n) > \alpha \rbrace ,\) 
